Unmanned aerial vehicle and truck cooperative distribution method considering battery replacement plan

Abstract

The application discloses a kind of unmanned aerial vehicle and truck collaborative distribution method considering battery replacement plan, applied to unmanned aerial vehicle and truck collaborative distribution goods field, first, the data of customer in warehouse distribution range is collected, according to the goods demand of customer and distribution distance classification, unmanned aerial vehicle customer group and truck customer group are constructed;Second, a mixed integer programming model considering unmanned aerial vehicle and truck collaborative distribution goods is constructed;Then, design battery allocation module, solve the optimal battery replacement plan in each iteration;Finally, the application obtains the optimal distribution path based on the adaptive large neighborhood search algorithm to solve truck and unmanned aerial vehicle collaborative distribution scheme;The technical scheme of the application can significantly reduce the total distribution cost, improve the flexibility of goods distribution, and provide a new solution for timely delivering goods to the designated location in the case of road traffic congestion.

Description

Technical Field

[0001] This invention belongs to the field of logistics and distribution technology, and specifically relates to a method for collaborative delivery of drones and trucks that takes into account battery replacement plans. Background Technology

[0002] In many cities, timely delivery services need to be provided to customers within the warehouse's delivery area every day. Since there are many customers scattered throughout the delivery area, and some goods need to be delivered from the warehouse to designated locations quickly due to quality requirements, it is necessary to carefully design delivery plans in order to improve the quality of delivery services while reducing operating costs and ensuring that goods can be delivered to their destination in a short time.

[0003] Traditional logistics delivery relies on trucks operating along predetermined routes, resulting in poor timeliness and frequent delays due to traffic congestion and unforeseen events, sometimes compromising the quality of goods. With the continuous development of modern technology, drones, as a key industry in technological innovation, are experiencing rapid growth. Compared to truck transportation, drones can fly at low altitudes, ignoring complex road conditions and unaffected by ground traffic, thus significantly shortening delivery times. While drones offer high speed and low cost per unit distance, their electric flight limits flight time and distance, whereas trucks have greater carrying capacity and longer driving range. Therefore, combining drones and trucks for joint delivery is a feasible approach. This combination effectively addresses the problems of truck delivery being severely affected by road traffic and the short flight range of drones, allowing them to complement each other. Furthermore, compared to existing patents on drone-truck collaborative delivery, this invention also considers optimal battery replacement and charging arrangements, making it more practical and applicable to real-world situations. Summary of the Invention

[0004] The purpose of this invention is to design a method for collaborative delivery between drones and trucks that takes into account battery replacement plans. This invention determines the optimal delivery route from the warehouse to each customer point while simultaneously considering drone payload limitations, battery range limitations, and maximum flight distance requirements. Using this method, the total number of batteries used can be reduced while minimizing total delivery costs, thus promoting urban environmental protection and emission reduction, and laying the foundation for the large-scale commercial application of drones.

[0005] To achieve the above, the technical solution of the present invention is as follows:

[0006] S1: Collect customer data within the warehouse delivery area, classify customers according to their cargo demand and delivery distance, and build drone customer groups and truck customer groups;

[0007] S2: Construct a mixed-integer programming model that considers the collaborative delivery of goods by drones and trucks;

[0008] S3: Design a battery distribution module to solve for the optimal battery replacement plan under each delivery scheme;

[0009] S4: Based on the adaptive large neighborhood search algorithm, a collaborative delivery scheme for trucks and drones is obtained, and the optimal delivery route is obtained.

[0010] The specific steps for step S1, building the drone customer base and truck customer base, are as follows:

[0011] S101: First, add customers whose cargo demand exceeds the drone's capacity limit to the truck customer group. middle;

[0012] S102: Randomly select one customer from the remaining customers, calculate whether the sum of the distances between the customer and the two nearest customers exceeds the maximum single flight distance limit of the drone. If it exceeds the maximum single flight distance limit, add the customer to the [unclear - likely a list of customers]. The process is repeated continuously until there are no more customers who meet the conditions.

[0013] S103: Add the remaining customers who do not meet the criteria to the drone customer group. middle.

[0014] The specific steps for step S2, which involves constructing a mixed-integer programming model that considers the collaborative delivery of goods by drones and trucks, are as follows:

[0015] S201: Before building the model, the entire logistics and distribution problem needs to be defined as follows:

[0016] (1) Each truck carries only one drone when it leaves the warehouse, and the drone is equipped with a battery.

[0017] (2) The truck leaves the warehouse with its drone. When the truck stops at any customer point, it can launch the drone to serve the customer. After the truck launches the drone and serves the customer at the current location, it immediately moves to the next customer point to wait for the drone to be retrieved. It does not visit other customers in between. After the drone serves a customer, it immediately lands at the retrieval point. The drone is not allowed to serve multiple customers in a single flight. After the truck and the drone have served a group of customers together, the truck returns to the warehouse with the drone to complete one truck trip.

[0018] (3) A truck route includes multiple truck trips;

[0019] (4) During the collaborative service between trucks and drones, drones are not allowed to land on other trucks for reasons such as airspace safety, so as to avoid safety issues.

[0020] S202: Set the objective function for total delivery cost as follows:

[0021]

[0022] The first objective function represents minimizing the total cost of truck transportation, which is the sum of the costs of the truck traveling along each route. The second objective function represents minimizing the charging cost of all batteries, which includes the charging cost of each battery at the depot after each use.

[0023] S203: Set the following flow constraints

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Specifically, formula (2) represents the truck flow balance constraint, formulas (3)-(4) ensure that each truck departs from the warehouse and eventually returns to the warehouse, formula (5) represents the relationship between two consecutive trips of the truck, formula (6) indicates that any customer must be served once, formula (7) ensures that a truck passes through the drone launch location, formula (8) guarantees flow balance at the drone service point, and formula (9) indicates that the truck goes directly from the drone launch point to the recovery point without passing through other customer points in between.

[0033] S204: Set the following time constraints

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Specifically, formula (10) represents the actual time when the truck arrives at the customer's location, formula (11) represents that the truck must arrive at the recycling point before the drone and wait there to recycle the drone, formulas (12)-(13) represent the time when the drone flies to its target customer's location and the time when it lands at the recycling point after serving the customer, formulas (14)-(15) represent the time when each battery leaves and returns to the station with the drone each time, formulas (16)-(17) construct the time recursion relationship of the time when the battery is used by the drone twice in a row, formulas (18)-(20) represent that the time when the drone and the truck arrive at their customers must be within the customer's time window, and formula (21) ensures that the truck's next trip from the warehouse is later than the time when the truck's previous trip ended and arrived at the warehouse.

[0047] S205: Set battery-related constraints

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Specifically, formula (22) represents the remaining battery power in the drone carried by the truck when it returns to the warehouse, formula (23) represents the energy consumption of the battery during the drone service, formula (24) represents that the drone can carry a maximum of one battery at a time, formula (25) represents the order in which the batteries are used consecutively, formula (26) represents that one battery is only loaded on one drone at a time, formula (27) limits the total number of batteries, and formula (28) constructs the relationship between variables;

[0056] S206: Setting Truck Capacity Constraints

[0057]

[0058] Specifically, this formula represents a recursive formula for the amount of cargo carried by a truck.

[0059] The specific steps for step S3, designing the battery allocation module and solving the optimal battery replacement plan for each distribution scheme, are as follows:

[0060] S301: The present invention defines the battery replacement plan as follows:

[0061] (1) After each trip, the truck returns to the warehouse with the drone, removes the battery from the drone and places it in the station to charge, and replaces the drone with another battery in the warehouse.

[0062] (2) In the event of insufficient battery quantity, the present invention allows batteries in the field to be installed in the drone before they are fully charged, which improves the flexibility of the overall scheduling plan.

[0063] S302: Establish a mixed-integer programming model for battery allocation. Solve the proposed battery allocation model at the end of each iteration to obtain the optimal battery arrangement plan. The objective function of this model is set as follows:

[0064]

[0065] The first term represents minimizing the number of batteries used, and the second term represents minimizing the charging cost of all batteries.

[0066] S303: Set the following constraints related to the battery replacement plan:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] Specifically, the above formulas represent the recursive expressions for the remaining power of the battery inside the drone and the charging amount of the battery at the station, respectively, and the total power consumption of the drone during each truck trip cannot exceed the remaining power of the battery it is currently carrying.

[0074] Step S4: The specific steps for obtaining the optimal delivery route by solving the truck and drone collaborative delivery scheme based on the adaptive large neighborhood search algorithm are as follows:

[0075] S401: This invention designs five deletion operators, namely, random deletion operator, worst-case deletion operator, similarity deletion operator, maximum travel time saving deletion operator, and maximum energy violation saving deletion operator; based on the weight of each deletion operator, a deletion operator is randomly selected using a roulette wheel to destroy the current solution, and the deleted customers are stored in the set ω;

[0076] S402: This invention designs five insertion operators: random insertion operator, greedy insertion operator, regret-K insertion operator, greedy insertion operator that minimizes duration, and insertion operator at the first feasible position. Based on the corrupted solution obtained in step S401, an insertion operator is randomly selected using a roulette wheel method according to the weights of each insertion operator. The customers in set ω are re-added to the current path, and the current solution is repaired to obtain a new solution S'.

[0077] S403: Compare the cost of S' with the cost of the optimal solution. If the cost of S' is smaller, then update both the optimal solution and the current solution to S'. If the cost of S' is greater than the cost of the optimal solution but less than the cost of the current solution, then update the current solution to S'. If the cost of S' is greater than the cost of the current solution, then determine whether to retain S' based on the simulated annealing criterion. If the criterion is satisfied, then update the current solution to S'.

[0078] S404: If the algorithm fails to obtain a better solution for N consecutive generations, the local neighborhood search strategy is invoked to optimize the current result. Specifically, the local neighborhood search strategy includes: swapping the order of two customers within a path, swapping the order of two customers between paths, and swapping several customers with the same position in the service sequence between paths. After executing the local neighborhood search strategy, the current solution is updated.

[0079] S405: If the maximum number of iterations is reached, output the optimal result. If the maximum number of iterations is not reached, update the weights of all deletion and insertion operators, return to S401 to continue the loop, and increment the number of iterations by 1.

[0080] Compared with the prior art, the advantages of the technical solution of the present invention are as follows:

[0081] This invention addresses the problem of collaborative goods delivery by drones and trucks by establishing a mixed-integer programming model that accurately characterizes the essence of the problem. It considers various real-world factors, making both the proposed problem and the constructed model closely reflect actual conditions and possessing strong practical application value. Furthermore, this invention generates initial solutions based on two modules: path generation and battery allocation. It proposes an adaptive large-neighborhood algorithm framework that incorporates multiple deletion operators, multiple insertion operators, and local neighborhood search. The algorithm exhibits strong applicability and high scalability, achieving good solution quality, and enabling efficient collaborative delivery tasks by trucks and drones.

[0082] Based on the above reasons, this invention can be widely promoted in the field of logistics and distribution. Attached Figure Description

[0083] Figure 1 This is a flowchart illustrating the implementation of the drone and truck collaborative delivery method of the present invention.

[0084] Figure 2 The flowchart of the adaptive large neighborhood algorithm of the present invention is shown below. Detailed Implementation

[0085] To further illustrate the above-mentioned objectives, features, and advantages of the present invention, the present invention will now be described in detail with reference to the accompanying drawings.

[0086] like Figure 1 As shown, the implementation process of the present invention includes the following steps:

[0087] S1: Collect customer data within the warehouse delivery area, classify customers according to their cargo demand and delivery distance, and build drone customer groups and truck customer groups;

[0088] Specifically, first, data is collected from each customer location, and the set of all customers is V. C Add customers whose cargo demand exceeds the drone's capacity limit to the list. middle;

[0089] Then, randomly select customer i from the remaining customers and determine V. C If the sum of the distances of arcs (i,j) and (i,k) to the two customers closest to customer i exceeds the maximum flight distance of the drone, then that customer cannot be served by the drone. Therefore, point i needs to be added to the drone's range. The process is repeated continuously until there are no more customers who meet the conditions.

[0090] Finally, add the remaining customers to the drone customer group.

[0091] S2: Construct a mixed-integer programming model that considers the collaborative delivery of goods by drones and trucks;

[0092] The variables used in the model and their corresponding definitions are shown in Table 1.

[0093] Table 1 defines the sets, parameters, and variables in the model.

[0094]

[0095]

[0096] This invention addresses the problem of collaborative goods delivery using drones and trucks, detailed as follows: The delivery model includes a warehouse, N customers requiring goods to be delivered by truck or drone, and K trucks and their onboard drones. The set of all points can be represented as: V = {0, 1, ..., N, N+1}, where 0 and N+1 represent warehouses, 0 represents the delivery start point, and N+1 represents the delivery end point. C = {1,2,…,N} represents the set of all customers. Each truck's journey starts from warehouse 0, serves a series of points, and returns to warehouse N+1 to complete the entire delivery process. The delivery network can be represented by a directed graph G = (V,A), where A = {(i,j)|i,j∈V} is the set of all arcs, V is the set of nodes, and V... P and V B Defined as V respectively C ∪{0}、V C ∪{N+1}; In this invention, all trucks and their onboard drones are initially stored in a warehouse. Each truck carries one drone to serve customers within its delivery range. Furthermore, a truck can launch its drone at any customer location. After serving the current customer, the truck immediately proceeds to a collection point to retrieve the drone, without stopping at any other points in between. During a truck's journey, the drone can be launched multiple times. After the drone and truck complete a delivery trip together, they return to the warehouse, where the drone's battery is removed, recharged, and replaced with a battery from the depot. This invention allows the newly replaced battery to be partially charged. The mixed-integer programming model proposed in this invention is as follows:

[0097] Set the objective function for total delivery cost as follows:

[0098]

[0099] The first objective function represents minimizing the total cost of truck transportation, and the second objective function represents minimizing the charging cost of all batteries.

[0100] Set the following flow constraints

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Specifically, formula (2) represents the truck flow balance constraint, formulas (3)-(4) ensure that each truck departs from the warehouse and eventually returns to the warehouse, formula (5) represents the relationship between two consecutive trips of the truck, formula (6) indicates that any customer must be served once, formula (7) ensures that a truck passes through the drone launch location, formula (8) guarantees flow balance at the drone service point, and formula (9) indicates that the truck goes directly from the drone launch point to the recovery point without passing through other customer points in between.

[0110] Set the following time constraints

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] Specifically, formula (10) represents the actual time when the truck arrives at the customer's location, formula (11) represents that the truck must arrive at the recycling point before the drone and wait there to recycle the drone, formulas (12)-(13) represent the time when the drone flies to its target customer's location and the time when it lands at the recycling point after serving the customer, formulas (14)-(15) represent the time when each battery leaves and returns to the station with the drone each time, formulas (16)-(17) construct the time recursion relationship of the time when the battery is used by the drone twice in a row, formulas (18)-(20) represent that the time when the drone and the truck arrive at their customers must be within the customer's time window, and formula (21) ensures that the truck's next trip from the warehouse is later than the time when the truck's previous trip ended and arrived at the warehouse.

[0124] Set battery-related constraints

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] Specifically, formula (22) represents the remaining battery power in the drone carried by the truck when it returns to the warehouse, formula (23) represents the energy consumption of the battery during the drone service, formula (24) represents that the drone can carry a maximum of one battery at a time, formula (25) represents the order in which the batteries are used consecutively, formula (26) represents that one battery is only loaded on one drone at a time, formula (27) limits the total number of batteries, and formula (28) constructs the relationship between variables;

[0133] The following truck capacity constraints are set. This formula represents the recursive formula for the number of packages carried by the truck. Formulas (30)-(35) are the range of values ​​for the variables.

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] S3: Design a battery distribution module to solve for the optimal battery replacement plan under each delivery scheme;

[0142] First, the present invention defines the battery replacement plan as follows:

[0143] (1) After each trip, the truck returns to the warehouse with the drone, removes the battery from the drone and places it in the station to charge, and replaces the drone with another battery in the warehouse.

[0144] (2) In the event of insufficient battery quantity, the present invention allows batteries in the field to be installed in the drone before they are fully charged, which improves the flexibility of the overall scheduling plan.

[0145] Then, a mixed-integer programming model for battery allocation is established. At the end of each iteration, the proposed battery allocation model is solved to obtain the optimal battery arrangement plan. In this model, 0-1 variables... This indicates that if battery m is carried by one truck for trip v, and then carried by another truck for trip u, the value is 1; Decision variable The remaining charge of battery m when it is carried by the truck on the journey u; decision variable. This indicates the battery level of battery m after the truck has completed its journey u;

[0146] Specifically, the objective function of this model is set as follows:

[0147]

[0148] The first term represents minimizing the number of batteries used, and the second term represents minimizing the charging cost of all batteries at the facility.

[0149] Set the following constraints related to the battery replacement plan:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] Specifically, the above formulas represent the recursive expressions for the remaining power of the battery inside the drone and the charging amount of the battery at the station, respectively, and the total power consumption of the drone during each truck trip cannot exceed the remaining power of the battery it is currently carrying.

[0157] S4: Based on the adaptive large neighborhood search algorithm, a collaborative delivery scheme for trucks and drones is obtained, and the optimal delivery route is obtained.

[0158] This invention proposes five deletion operators and five insertion operators, and the detailed application methods of these operators are as follows:

[0159] The first type of deletion operator, namely the random deletion operator:

[0160] The operator randomly removes q customers from the truck and drone paths and adds them to the deletion set ω;

[0161] The second type of deletion operator, namely the worst-case deletion operator:

[0162] This operator evaluates the cost reduction caused by deleting a point, and deletes the customer with the greatest cost reduction. The algorithm iterates until it is satisfied that q customers are deleted.

[0163] The third type of deletion operator is the similarity deletion operator:

[0164] The operator randomly selects a customer to delete, and uses the similarity function R. i,j =|AT i -AT j |-t i,j -S i Evaluate the point most similar to the given point, delete the most similar point j, then delete the next point most similar to j k, and so on, until q customers are deleted;

[0165] The fourth type of deletion operator is the maximum travel time saving deletion operator:

[0166] The time saving caused by removing customers is calculated as ΔD(u j ,i)=D(u j ,i)-D'(u j i), the operator deletes the customer who saves the most time.

[0167] The fifth deletion operator, namely the maximum energy violation of the economical deletion operator:

[0168] Find the battery with the largest energy violation, remove the truck trip u in its service sequence that consumes the most battery power from the drones, that is, remove all drone service points on trip u and add them to the set ω, until the battery has no energy violation; iterate the above process until it satisfies the condition of removing q customers or all batteries having no energy violations;

[0169] The first type of insertion operator, namely the random insertion operator:

[0170] This operator selects a customer from the set ω and arbitrarily inserts it into the path of a truck or drone;

[0171] The second type of insertion operator is the greedy insertion operator:

[0172] This operator selects a customer from the set ω and greedily inserts it into the position where the cost increase is minimal.

[0173] The third type of insertion operator is the regret-K insertion operator:

[0174] In this invention, k is set to 2. The operator calculates the cost increase for optimal insertion and the cost increase for suboptimal insertion of each customer in the set ω, calculates the difference between the two increases, selects the customer with the largest difference, and inserts it into the optimal position; then the cost difference between optimal insertion and suboptimal insertion of the remaining customers is recalculated, and so on, until all customers are inserted into the path;

[0175] The fourth insertion operator, even the greedy insertion operator with the shortest duration:

[0176] The purpose of this operator is to insert the customer into the position that minimizes the increase in the duration of the truck trip u;

[0177] The fifth insertion operator, namely the insertion operator at the first feasible position:

[0178] The purpose of this operator is to insert customers of the drone service. Under the premise of ensuring the time window constraint of the insertion point, if the power consumption caused by inserting the point is less than the maximum allowable power consumption of the truck trip, then insert it at the first feasible point position, and so on, to ensure that all points in the set ω are inserted into the solution.

[0179] The process of finding the optimal path using the adaptive large neighborhood algorithm is as follows: Figure 2 As shown, the specific steps are as follows:

[0180] Step 1: Based on the weights of each operator, randomly select a deletion operator using a roulette wheel to disrupt the current path. Store the deleted customers in set ω. Then, in the same way, select an insertion operator and add the customers in set ω back into the current path to obtain a new solution S'.

[0181] Each delete and insert operation has a selection weight w i In each iteration, the probability of an operator being selected is determined according to the following formula:

[0182]

[0183] Step 2: Compare the cost of the new solution S' with the cost of the optimal solution. If the cost of the new solution S' is smaller, then update both the optimal solution and the current solution to the new solution S'. If the cost of the new solution S' is greater than the cost of the optimal solution but less than the cost of the current solution, then update the current solution to the new solution S'. If the cost of the new solution S' is greater than the cost of the current solution, then determine whether to retain the new solution S' based on the simulated annealing criterion. If the criterion is satisfied, then update the current solution to the new solution S'.

[0184] Step 3: If a better solution has been obtained within N generations, skip to step 4; the current step does not need to be executed. If no better solution has been obtained for N consecutive generations, the local neighborhood search strategy is invoked to optimize the current result. Specifically, the local neighborhood search strategy includes: swapping the order of two customers within a path, swapping the order of two customers between paths, and swapping several customers with the same position in the service sequence between paths. After executing the local neighborhood search strategy, the current solution is updated.

[0185] Step 4: If the maximum number of iterations is reached, output the optimal result. If the maximum number of iterations is not reached, return to Step 1 to continue the loop, increment the iteration count by 1, and update the operator weights. The specific method is as follows:

[0186]

[0187] Wherein, the parameter θ represents the coefficient for updating the weighting based on the score of deletion and insertion operations, and the value of θ ranges from 0 to 1. ρ i π represents the number of times each operation occurs during the iteration process. i This represents the score of each operation during the iteration process. Specifically: when a new optimal solution is obtained, the score is 10; when a solution that is not optimal but is better than the current solution is obtained, the score is 5; and when the obtained solution is worse than the current solution but is selected based on the simulated annealing mechanism, the score is 1.

[0188] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A drone-truck collaborative delivery method considering a battery replacement program, characterized in that, Includes the following steps: S1: Collect customer data within the warehouse delivery area, classify customers according to their cargo demand and delivery distance, and build drone customer groups and truck customer groups; S2: Construct a mixed-integer programming model that considers the collaborative delivery of goods by drones and trucks; S3: Design a battery distribution module to solve for the optimal battery replacement plan under each delivery scheme; S4: The optimal delivery route for truck and drone collaboration is obtained based on the adaptive large neighborhood search algorithm; The specific steps for building a customer base for drones and trucks are as follows: S101: First, add customers whose cargo demand exceeds the drone's capacity limit to the truck customer group; S102: Randomly select a customer from the remaining customers and calculate whether the sum of the distances between the customer and the two nearest customers exceeds the maximum single flight distance of the drone. If it exceeds the maximum single flight distance, add the customer to the truck customer group. Continue to select customers from the remaining customers and perform the above operation until the sum of the distances between all remaining customers and the two nearest customers does not exceed the maximum single flight distance of the drone. S103: Add the remaining customers after step S102 to the drone customer group; The specific steps for designing a battery distribution module and solving for the optimal battery replacement plan under each distribution scheme are as follows: S301: The battery replacement plan is defined as follows: (1) After each trip, the truck returns to the warehouse with the drone, removes the battery from the drone and places it in the station to charge, and replaces the drone with another battery in the warehouse. (2) In the event of insufficient battery quantity, it is permissible to install batteries from the site into the UAV before they are fully charged; S302: Establish a mixed-integer programming model for battery allocation. Solve the proposed battery allocation model at the end of each iteration to obtain the optimal battery arrangement plan. The objective function of this model is set as follows: ， In the formula, the first term represents minimizing the number of batteries used, and the second term represents minimizing the charging cost of all batteries; S303: Set the following constraints related to the battery replacement plan: ， ， ， ， ， 。 2. The drone-truck collaborative delivery method considering battery replacement plans according to claim 1, characterized in that, The specific steps for designing an adaptive large neighborhood search algorithm to solve the truck and drone collaborative delivery route planning scheme considering a battery replacement plan and to obtain the optimal delivery route are as follows: S401: In each iteration, a roulette wheel is used to select an operator from a variety of deletion operators to destroy the current solution, and the same method is used to select an insertion operator from a variety of insertion operators to repair the destroyed solution; S402: Use simulated annealing to determine whether the solution obtained after each iteration is acceptable; S403: If the algorithm fails to obtain a better solution for several consecutive generations, the local neighborhood search strategy is invoked to update the current solution.

Images